I'm wondering if any PCI card will work - right now, your compu doesn't have to drive any power to the PCI bus... not sure.
I can't answer your questions, but I'd maybe experiment with an older, cheaper card, such as a Radeon VE, both which would work fine w/ MAME. The slower the core memory and engine clock, the less power is required.
The good news is that the video won't draw peak power on bootup, which is the only time that you should need all 160 watts (most power supplies are rated at the peak rating, and don't need to supply anywhere near that once booted up).